Stability analysis on solitary wave solutions for systems of nonlinear wave equations

• Project/Area Number: 21540163
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Saitama University
• Principal Investigator: OHTA Masahito 埼玉大学, 大学院・理工学研究科, 准教授 (00291394)
• Co-Investigator(Renkei-kenkyūsha): KOIKE Shigeaki 埼玉大学, 大学院・理工学研究科, 教授 (90205295) ; NAGASAWA Takeyuki 埼玉大学, 大学院・理工学研究科, 教授 (70202223) ; MACHIHARA Shuji 埼玉大学, 教育学部, 准教授 (20346373)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 非線形偏微分方程式 / 非線形シュレディンガー方程式 / 非線形波動方程式 / 孤立波 / 定在波 / 安定性 / 不安定性 / 非線形シュレデインガー方程式 / 軌道安定性 / 変分問題

Research Abstract

We improved the standard theory on instability of standing wave solutions for nonlinear Schrodinger equations. In particular, we proved a new instability result for a borderline case between stability and instability. Moreover, we applied the abstract theory to a system of nonlinear Schrodinger equations related to the Raman amplification in plasma. Furthermore, under a general condition, we proved that linear instability implies nonlinear instability.

Research Products

• [Journal Article] Bifurcation from semitrivial standing waves and ground states for a system of nonlinear Schrodinger equations (2012)
  • Author(s): M. Colin, M. Ohta
  • Journal Title: SIAM Journal on Mathematical Analysis Volume: 44 Pages: 206-223
  • Peer Reviewed
• [Journal Article] Instability of bound states for abstract nonlinear Schrodinger equations (2011)
  • Author(s): M. Ohta
  • Journal Title: Journal of Functional Analysis Volume: 261 Pages: 90-110
  • Peer Reviewed
• [Journal Article] Stability of standing waves for the Klein-Gordon-Schrodinger system (2010)
  • Author(s): H. Kikuchi, M. Ohta
  • Journal Title: Journal of Mathematical Analysis and Applications Volume: 365 Pages: 109-114
• [Journal Article] Stability of standing waves for the Klein-Gordon-Schrodinger system (2010)
  • Author(s): Hiroaki Kikuchi, Masahito Ohta
  • Journal Title: Journal of Mathematical Analysis and Application Volume: 365 Pages: 109-114
  • Peer Reviewed
• [Journal Article] Stability of standing waves for nonlinear Schrodinger equation with attractive delta potential and repulsive nonlinearity (2009)
  • Author(s): M. Kaminaga, M. Ohta
  • Journal Title: Saitama Mathematical Journal Volume: 26 Pages: 39-48
  • Peer Reviewed
• [Journal Article] Instability of standing waves for a system of nonlinear Schrodinger equations with three-wave interaction (2009)
  • Author(s): M. Colin, Th. Colin, M. Ohta
  • Journal Title: Funkcialaj Ekvacioj Volume: 52 Pages: 371-380
  • Peer Reviewed
• [Journal Article] Stability of solitary waves for a system of nonlinear Schrodinger equations with three wave interaction (2009)
  • Author(s): M. Colin, Th. Colin, M. Ohta
  • Journal Title: Annales de l'Institut Henri Poincare, Analyse Non Lineaire Volume: 26 Pages: 2211-2226
  • Peer Reviewed
• [Journal Article] Remarks on global existence and blowup for damped nonlinear Schrodinger equations (2009)
  • Author(s): M. Ohta, G. Todorova
  • Journal Title: Discrete and Continuous Dynamical Systems Volume: 23 Pages: 1313-1325
  • Peer Reviewed
• [Journal Article] Stability of solitary waves for a system of nonlinear Schrodinger equations with three wave interaction (2009)
  • Author(s): M.Colin, T.Colin, M.Ohta
  • Journal Title: Ann.Inst.H.Poincare, Anal.Non Lineaire 26 Pages: 2211-2226
  • Peer Reviewed
• [Journal Article] Instability of standing waves for a system of nonlinear Schrodinger equations with three-wave interaction (2009)
  • Author(s): M.Colin, T.Colin, M.Ohta
  • Journal Title: Funkcialaj Ekvacioj 52 Pages: 371-380
  • Peer Reviewed
• [Journal Article] Stability of standing waves for nonlinear Schrodinger equation with attractive delta potential and repulsive nonlinearity (2009)
  • Author(s): M.Kaminaga, M.Ohta
  • Journal Title: Saitama Mathematical Journal 26 Pages: 39-48
  • Peer Reviewed
• [Presentation] 非線形シュレディンガー方程式系の定在波の安定性 (2012)
  • Author(s): 太田雅人
  • Organizer: 第61回理論応用力学講演会
  • Place of Presentation: 東京大学生産技術研究所
  • Year and Date: 2012-03-07
• [Presentation] 非線形波動方程式系の定在波の安定性 (2012)
  • Author(s): 太田雅人
  • Organizer: 第61回理論応用力学講演会
  • Place of Presentation: 東京大学生産技術研究所(招待講演)
  • Year and Date: 2012-03-07
• [Presentation] Stability of standing waves for a system of nonlinear Schrodinger equations (2011)
  • Author(s): 太田雅人
  • Organizer: 第9回浜松偏微分方程式研究集会
  • Place of Presentation: 静岡大学工学部
  • Year and Date: 2011-12-27
• [Presentation] Stability of standing waves for a system of nonlinear Schrodinger equations (2011)
  • Author(s): 太田雅人
  • Organizer: 弘前非線形方程式研究会
  • Place of Presentation: 弘前大学
  • Year and Date: 2011-12-23
• [Presentation] Stability of standing waves for a system of nonlinear Schrodinger equations (2011)
  • Author(s): M. Ohta
  • Organizer: Stability problems in nonlinear dispersive PDEs
  • Place of Presentation: University de Cergy-Pontoise, France
  • Year and Date: 2011-11-24
• [Presentation] Stability of standing waves for a system of nonlinear Schrodinger equations in a critical case (2011)
  • Author(s): 太田雅人
  • Organizer: Linear and Nonlinear Waves No.9
  • Place of Presentation: ピアザ淡海
  • Year and Date: 2011-11-04
• [Presentation] Standing waves for a system of nonlinear Schrodinger equations (2011)
  • Author(s): M. Ohta
  • Organizer: One Forum, Two Cities : Aspect of Nonlinear PDEs
  • Place of Presentation: National Taiwan University
  • Year and Date: 2011-09-01
• [Presentation] Standing waves for a system of nonlinear Schrodinger equations (2011)
  • Author(s): M. Ohta
  • Organizer: 第36回偏微分方程式論札幌シンポジウム
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-08-24
• [Presentation] Nonlinear instability of linearly unstable standing waves for nonlinear Schrodinger equations (2011)
  • Author(s): 太田雅人
  • Organizer: OCAMI楕円型方程式研究集会-定常非線形シュレディンガー方程式の定在波解の研究-
  • Place of Presentation: 大阪市立大学
  • Year and Date: 2011-08-11
• [Presentation] Nonlinear instability of linearly unstable standing waves for nonlinear Schrodinger equations (2010)
  • Author(s): Masahito Ohta
  • Organizer: Seminaire de l'equipe MIP, Institut de Mathematiques de Toulouse
  • Place of Presentation: University of Paul Sabatier, France
  • Year and Date: 2010-10-19
• [Presentation] Stability of standing waves for a system of NLS with a three-wave interaction (2009)
  • Author(s): M. Ohta
  • Organizer: The second Chile-Japan workshop on nonlinear elliptic and parabolic PDEs
  • Place of Presentation: 明治大学
  • Year and Date: 2009-12-01
• [Presentation] Stability of standing waves for a system of NLS with a three-wave interaction (2009)
  • Author(s): Masahito Ohta
  • Organizer: he second Chile-Japan Workshop on Nonlinear Elliptic and Parabolic PDEs
  • Place of Presentation: 明治大学紫紺館(東京)
  • Year and Date: 2009-12-01
• [Presentation] Stability of standing waves for some systems of nonlinear Schrodinger equations with three-wave interactions (2009)
  • Author(s): M. Ohta
  • Organizer: The 7th International ISAAC Congress
  • Place of Presentation: Imperial College London, UK
  • Year and Date: 2009-07-14
• [Remarks]
  • URL: http://www.rimath.saitama-u.ac.jp/lab.jp/MasahitoOhta.html
• [Remarks]
  • URL: http://www.rimath.saitama-u.ac.jp/lab.jp/MasahitoOhta.html
• [Remarks]
  • URL: http://www.rimath.saitama-u.ac.jp/lab.jp/MasahitoOhta.html